This invention relates to sonic well logging used in the hydrocarbon well exploration. More particularly, the invention relates to methods for processing sonic well log waveforms.
Sonic logging of wells is well known in hydrocarbon exploration. Sonic well logs are generated using sonic tools typically suspended in a mud-filled borehole by a cable. The sonic logging tool typically includes a sonic source (transmitter), and a plurality of receivers (receiver array) that are spaced apart by several inches or feet. It is noted that a sonic logging tool may include a plurality of transmitters and that sonic logging tools may be operated using a single transmitter (monopole mode), dual transmitters (dipole mode) or a plurality of transmitters (multipole mode). A sonic signal is transmitted from the sonic source and detected at the receivers with measurements made every few inches as the tool is drawn up the borehole. The sonic signal from the transmitter enters the formation adjacent to the borehole and part of the sonic signal propagates in the borehole.
Sonic waves can travel through formations around the borehole in essentially two forms: body waves and surface waves. There are two types of body waves that travel in formation: compressional and shear. Compressional waves, or P-waves, are waves of compression and expansion and are created when a formation is sharply compressed. With compressional waves, small particle vibrations occur in the same direction the wave is traveling. Shear waves, or S-waves are waves of shearing action as would occur when a body is struck from the side. In this case, rock particle motion is perpendicular to the direction of wave propagation.
Surface waves are found in a borehole environment as complicated borehole-guided waves coming from reflections of the source waves reverberating in the borehole. The most common form of surface wave is the Stoneley wave. In situations where dipole (directional) sources and receivers are used, an additional flexural wave propagates along the borehole and is caused by the flexing action of the borehole in response to the dipole signal form the source. It is noted that sonic waves also will travel through the fluid in the borehole and along the tool itself. With no interaction with the formation, these waves do not provide useful information and may interfere with the waveforms of interest.
Typically, compressional (P-wave), shear (S-wave) and Stoneley arrivals are detected by the receivers. The speeds at which these waves travel through the rock are controlled by rock mechanical properties such as density and elastic dynamic constants, and other formation properties such as amount and type of fluid present in the rock, the makeup of the rock grains and the degree of intergrain cementation. Thus by measuring the speed of sonic wave propagation in a borehole, it is possible to characterize the surrounding formations by parameters relating to these properties. The information recorded by the receivers is typically used to determine formation parameters such as formation slowness (the inverse of sonic speed) from which pore pressure, porosity, and other determinations can be made. The speed or velocity of a sonic wave is often expressed in terms of 1/velocity and is called “slowness.” Since the tools used to make sonic measurements in boreholes are of fixed length, the difference in time (ΔT) taken for a sonic wave to travel between two points on the tool is directly related to the speed/slowness of the wave in the formation. In certain tools such as the DSI™ (Dipole Sonic Imager) tool (a trademark owned by Schlumberger), the sonic signals may be used to image the formation.
Details relating to sonic logging and log processing techniques are set forth in U.S. Pat. No. 4,131,875 to Ingram; U.S. Pat. No. 4,594,691 to Kimball and Marzetta; U.S. Pat. No. 5,278,805 to Kimball; U.S. Pat. No. 5,831,934 to Gill et al.; A. R. Harrison et al., “Acquisition and Analysis of Sonic Waveforms From a Borehole Monopole and Dipole Source . . . ” SPE 20557, pp. 267-282 (September 1990); and C. V. Kimball and T. L. Marzetta, “Semblance Processing of Borehole Acoustic Array Data”, Geophysics, Vol. 49, pp. 274-281 (March 1984), all of which are incorporated by reference herein in their entireties.
The response of any given one of receivers to a sonic signal from a transmitter is typically a waveform as shown in FIG. 1 for an eight-receiver array. Sonic waveforms 1 through 8 as received at different receivers within the array are shown. The responses of the several receivers are staggered in time due to the different spacing of the receivers from the transmitter. The first arrivals 10 shown are compressional waves, followed by the arrival of shear waves 12 and then the arrival of Stoneley waves 14. It will be appreciated that where the sonic signal detected is non-dispersive (e.g. P-waves and S-waves), the signal obtained at each receiver will take the same or similar form. However, where the sonic signal is dispersive (e.g. Stoneley and flexural waves), the signal obtained at the different receivers will appear different.
In most formations, the sonic speeds in the tool and the wellbore mud are less than the sonic speed in the formation. In this typical situation, the compressional (P-waves), shear (S-waves), and Stoneley or tube wave arrivals and waves are detected by the receivers and are processed. Sometimes, the sonic speed in the formation is slower than the drilling mud; i.e., the formation is a “slow” formation. In this situation, there is no refraction path available for the shear waves, and typically shear (S-waves) arrivals are not measurable at the receivers. However, the shear slowness of the formation is still a desirable formation parameter to obtain. Although without shear wave signal detection, direct measurement of formation shear slowness is not possible but it may be determined from other measurements.
One way to obtain the slowness of a formation from an array of sonic waveforms is to use slowness-time-coherence (STC) processing. One type of STC processing is presented in U.S. Pat. No. 4,594,691, incorporated herein in its entirety. STC processing is a full waveform analysis technique that aims to find all propagating waves in a composite waveform. The result of the process is a collection of semblance peaks in a slowness-time plane for various depths. At each depth the peaks may be associated with different waveform arrivals. The processing adopts a semblance algorithm to detect arrivals that are coherent across the array of receivers and estimates their slowness. The basic algorithm advances a fixed-length time window across the waveforms in small overlapping steps through a range of potential arrival times. For each time position, the window position is moved out linearly in time, across the array of receiver waveforms, beginning with a moveout corresponding to the fastest wave expected and stepping to the slowest wave expected. For each moveout, a coherence function is computed to measure the similarity of the waves within the window. When the window time and the moveout correspond to the arrival time and slowness of a particular component, the waveforms within the window are almost identical, yielding a high value of coherence. In this way, the set of waveforms from the array is examined over a range of possible arrival times and slownesses for wave components.
STC processing produces coherence (semblance) contour plots in the slowness/arrival time plane. The semblance function relates the presence or absence of an arrival with a particular slowness and particular arrival time. If the assumed slowness and arrival time do not coincide with that of the measured arrival, the semblance takes on a smaller value. Consequently, arrivals in the received waveforms manifest themselves as local peaks in a plot of semblance versus slowness and arrival time. These peaks are typically found in a peak-finding routine discussed in the aforementioned article by Kimball and Marzetta.
As the output of STC processing is a coherence plot, the coherence of each arrival can be used as a quality indicator, higher values implying greater measurement repeatability. When processing dipole waveforms, one of the coherence peaks will correspond to the flexural mode but with a slowness that is always greater (slower) than the true shear slowness. A precomputed correction is used to remove this bias.
In simple STC processing, all receiver stations are considered. Another type of slowness-time-coherence is processing multi-shot slowness-time-coherence (MSTC) processing wherein sub-arrays of receiver stations within the receiver array are considered. MSTC processing is described in U.S. patent application Ser. No. 09/678,454, incorporated herein by reference in its entirety.
In the aforementioned methods, the same back-propagation and stacking techniques are used regardless of whether the wave being analyzed is a P-wave, S-wave, or a Stoneley wave; i.e., regardless of whether the wave is non-dispersive or dispersive. Additional techniques are known to address dispersive waves. For dispersive waves, STC processing is modified to take into account the effect of frequency and dispersion.
Bias-corrected STC as described in U.S. Pat. No. 5,229,939, incorporated herein in its entirety, involves processing the flexural waveform using STC methods but correcting the non-dispersive processing results by a factor relating to the measured slowness and hole diameter, that is, post-processing the STC results. In particular, correction values are obtained by processing model waveforms with the STC techniques and comparing the measured slowness with the formation shear slowness of the model.
A second technique to provide slowness logging which accounts for dispersion is known as Dispersive Slowness Time Coherence (DSTC) processing or Quick DSTC (QDSTC) and presented in U.S. Pat. No. 5,278,805, the contents of which are incorporated herein by reference. DTSC processing broadly comprises back-propagating detected dispersive waveforms in the Fourier domain while accounting for dispersion and then stacking the processed waveforms. DSTC processing has the ability to be applied to non-dispersive waves such as monopole compressional or shear waves, Since the first step required for DSTC processing is the calculation or selection or an appropriate dispersion curve, all that is required is a dispersion curve that represents a non-dispersive wave, i.e., a flat “curve”.
The first step in slowness-time coherence processing is computing semblance, a two-dimensional function of slowness and time, generally referred to as the STC slowness-time plane. The semblance is the quotient of the beamformed energy output by the array at slowness p (the “coherent energy”) divided by the waveform energy in a time window of length T (the “total energy”). The semblance function is given by Equation (1) where xi(t) is the waveform recorded by the i-th receiver of an M-receiver equally spaced array with inter-receiver spacing ΔZ. The array of waveforms {xi(t)} acquired at depth z constitutes a single frame of data.
                              ρ          ⁡                      (                          τ              ,              p                        )                          =                                            ∫              τ                              τ                +                τ                                      ⁢                                                            [                                                            ∑                                              i                        =                        0                                                                    M                        -                        1                                                              ⁢                                                                  x                        i                                            ⁡                                              (                                                  t                          +                                                      i                            ⁢                                                                                                                  ⁢                            Δ                            ⁢                                                                                                                  ⁢                            z                            ⁢                                                                                                                  ⁢                            p                                                                          )                                                                              ]                                2                            ⁢                              ⅆ                t                                                          M            ⁢                                                  ⁢                                          ∫                τ                                  τ                  +                  τ                                            ⁢                                                ∑                                      i                    =                    0                                                        M                    -                    1                                                  ⁢                                                                            [                                                                        x                          i                                                ⁡                                                  (                                                      t                            +                                                          i                              ⁢                                                                                                                          ⁢                              Δ                              ⁢                                                                                                                          ⁢                              z                              ⁢                                                                                                                          ⁢                              p                                                                                )                                                                    ]                                        2                                    ⁢                                      ⅆ                    t                                                                                                          (        1        )            The semblance ρ(τ,p) for a particular depth z is a function of time τ and slowness p.
A second step is identifying peaks corresponding to high coherence on the slowness-time plane. Peaks are identified by sweeping the plane with a peak mask. The peak mask is a parallelogram having a slope that corresponds to the transmitter-receiver spacing. A peak is defined as a maximum within the mask region. For each peak, five variables are recorded: the slowness coordinate p, the time coordinate τ, the semblance ρ(τ,p), the coherent energy (the numerator of Equation 1), and the total energy (the denominator of Equation 1).
Peaks in coherence values signify coherent arrivals in the waveforms. For each depth, a contour plot of coherence as a function of slowness and time, referred to the slowness-time plane, can be made. Classification occurs when the slowness and arrival time at each coherence peak are compared with the propagation characteristics expected of the arrivals being sought and the ones that best agree with these characteristics are retained.
A “track” is defined by a Sequence of measurements over depth and “tracking” involved associating measurements made at one depth with measurements made at other depths. Typically in prior art methods the slowness and arrival time at each coherence peak arc compared with the propagation characteristics of the expected arrivals and classified as to type of arrival and “labeled” or “tacked” as corresponding to compressional (P-wave), shear (S-wave) or Stoneley waveform arrivals. Thus classified, the arrivals produce a continuous log of slowness versus depth, referred to as a “track”, a sequence of measurements composed of peaks identified as belonging to the same arrival as shown in FIG. 2. Referring to FIG. 2, peak 20 is classified as a compressional arrival and peak 22 is classified as a shear arrival and the classified peaks are joined to other arrivals of the same waveform in a slowness versus depth log. In prior art methods, the tracking composed two distinct steps 1) joining the peaks corresponding to the same waveform arrival in the track-search step to compose a “track”, and 2) identifying the tracks by a name through classification of the tracks. In these methods, individual peaks required classification independent of the tracks.
Correct tracking of the peaks is a difficult process for a number of reasons. Some of the peaks may correspond to spatial aliases rather than the arrival of real waveforms. Some of the peaks may actually be two peaks close together. In general, a shortcoming with prior art methods for tracking is that small changes in sonic waveform data can cause large differences in the final classification.
In a classification method referred to as local classification and described in U.S. patent application Ser. No. 09/591,405 (hereinafter '405), the peaks are classified by referring to only two levels, the current level and the previous level. This local classification of peaks of the tracks is independent of other non-adjacent peaks. Such a classification, because of the limits of the Bayesian algorithm used, does not classify the whole track but just the adjacent peaks of the track at any particular time. These classified peaks are used to generate a track and the track classified based on the classification of the peaks from which it is composed. The '405 method has the advantage of allowing classification to follow the usual data flow of the Integrated Slowness Determination Process (ISDP) processing and is applicable to well site implementation. Nevertheless in some situations local classification is not robust enough nor can defects like jumps between two tracks corresponding to different arrivals or splices on the final log be avoided. There are situations in which a different means of classification is desirable.